There are two distinct types of infinite loops: loops with no net change and loops with net change. Infinite loops contrast to controlled loops, which instead are maintained by a player intentionally repeating a set of actions or making the same decisions, rather than forced by game mechanics.

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Loops with no net change

These occur when a series of mandatory actions repeat after each other in a cycle, and there is no net change after each cycle, such that the game state is identical at the beginning and end of any cycle.

These types of infinite loops are illegal in gameplay, meaning that a player may not voluntarily activate any card if its activation would cause such a loop. If such a loop is caused by something involuntary, such as a player conducting their normal draw or a mandatory effect, then the card ruled to be the source of the infinite loop is automatically destroyed by game mechanics.

Pole Position

The mechanics of "Pole Position" naturally lend itself to causing such infinite loops when combined with Spell effects that directly or indirectly change a monster's ATK (see Card Rulings:Pole Position for further examples).

"Muka Muka" is now the monster on the field with the highest ATK, so "Pole Position" makes it unaffected by Spell Cards.

"Muka Muka" is now unaffected by "Axe of Despair", reducing its ATK to 900.

"Muka Muka" is now no longer the monster on the field with the highest ATK, so it is no longer unaffected by Spell Cards.

"Axe of Despair" now increases the ATK of "Muka Muka" by 1000, to 1900.

"Muka Muka" is now the monster on the field with the highest ATK, so "Pole Position" makes it unaffected by Spell Cards.

The above sequence would repeat infinitely, with the ATK of "Muka Muka" never settling.

Since this loop was caused by a mandatory action, it cannot be prevented by restricting the player's actions. Since the loop cannot be avoided, "Pole Position" will be destroyed by game mechanics.[1]

Amplifier

The mechanics of "Amplifier" naturally lend itself to causing such infinite loops when combined with Trap effects on the field that change control of "Jinzo" or negate the effect of "Jinzo" or Trap Cards (see Card Rulings:Amplifier for the official examples).

"The Emperor's Holiday" negates the effect of "Snatch Steal" ("Amplifier" cannot be negated).

Since "Snatch Steal" is now negated, control of "Jinzo" returns to its owner Player 2.

Since Player 2 now controls "Jinzo" (which is equipped with "Amplifier"), it negates the effect of Player 1's "The Emperor's Holiday".

Since "The Emperor's Holiday" is now negated, "Snatch Steal" is no longer negated, so Player 1 takes control of "Jinzo".

Since Player 1 now controls "Jinzo" (which is equipped with "Amplifier"), it no longer negates the effect of Player 1's "The Emperor's Holiday".

"The Emperor's Holiday" negates the effect of "Snatch Steal" ("Amplifier" cannot be negated).

The above sequence would repeat infinitely, with the player who controls "Jinzo" never settling.

Since this loop was caused by a mandatory effect, it cannot be prevented by restricting the player's actions. Since the loop cannot be avoided, whichever card is identified as the cause will be destroyed by game mechanics (no official ruling has been issued as to which is the cause).

"Mind Control" stops applying, so control of "Jinzo" returns to Player 1.

Since Player 1 now controls "Jinzo", "Amplifier" no longer prevents "Jinzo" from negating "Royal Decree", and prevents "Jinzo" from negating "Skill Drain".

Since it is no longer being negated, "Skill Drain" negates the effect of "Jinzo".

Since "Jinzo" is no longer negating "Royal Decree", "Royal Decree" negates the effect of "Skill Drain".

Since "Skill Drain" is no longer negating "Jinzo", "Jinzo" negates the effect of "Royal Decree".

Since "Royal Decree" is no longer negating "Skill Drain", "Skill Drain" negates the effect of "Jinzo".

The above sequence would repeat infinitely, with which effect is active never settling.

Since this loop was caused by a mandatory effect, it cannot be prevented by restricting the player's actions. Since the loop cannot be avoided, whichever card is identified as the cause will be destroyed by game mechanics (no official ruling has been issued as to which is the cause).

Cyber Blader

This loop only applies in the TCG. In the OCG, "Cyber Blader" can only negate activated effects.

Voluntary

If Player 2 attempts to Summon "Cyber Blader", the following would occur:

Since Player 1 controls three monsters, the effect of "Cyber Blader" negates the effect of "Snatch Steal". The equipped monster returns to Player 2's control.

Since Player 1 now controls two monsters, the effect of "Cyber Blader" instead doubles its ATK. The effect of "Snatch Steal" is no longer negated, so Player 1 gains control of the equipped monster.

Since Player 1 now controls three monsters, the effect of "Cyber Blader" negates the effect of "Snatch Steal". The equipped monster returns to Player 2's control.

The above sequence would repeat infinitely, with the player who controls the monster equipped with "Snatch Steal" never settling.

Therefore, it is an illegal move for Player 2 to Summon "Cyber Blader".

If Player 2 had already controlled "Cyber Blader" before Player 1 activated "Snatch Steal", then Player 1 activating "Snatch Steal" (targeting a monster other than "Cyber Blader") would be an illegal move.

Since Player 1 controls three monsters, the effect of "Cyber Blader" negates the effect of "Snatch Steal". The equipped monster returns to Player 2's control.

Since Player 1 now controls two monsters, the effect of "Cyber Blader" instead doubles its ATK. The effect of "Snatch Steal" effect is no longer negated, so Player 1 gains control of the equipped monster.

Since Player 1 now controls three monsters, the effect of "Cyber Blader" negates the effect of "Snatch Steal". The equipped monster returns to Player 2's control.

The above sequence would repeat infinitely, with the player who controls the monster equipped with "Snatch Steal" never settling.

Since this loop was caused by a mandatory effect, it cannot be prevented by restricting the player's actions. Since the loop cannot be avoided, whichever card is identified as the cause will be destroyed by game mechanics (no official ruling has been issued, but it will likely be either "Snatch Steal" or "Cyber Blader").

Loops with net change

Unlike loops with no net change, loops with net change cause a change to occur each time the cycle repeats. In these cases, the loop will continue until either the Duel ends or it ceases to have net change; if the latter, at this point the card ruled to have begun the loop will be automatically destroyed by game mechanics.

All-Out Attacks

All-Out Attacks OTKs utilize a loop with net change to force the opponent to continuously thin their Deck (either by drawing cards or sending cards from the Deck to the Graveyard), eventually resulting in a Deck out.

Player 1's face-down monsters will be flipped face-up, causing both their effects to activate.

The effect of "Hiro's Shadow Scout" will make the opponent draw 3 cards.

The effect of "Morphing Jar #2" will return both flipped monsters back to the Deck, and Player 1 will then reveal cards from the top of his/her Deck until revealing two monsters. Since the only two monsters in Player 1's Deck are the two that were just returned, they will be the ones revealed.

The two revealed monsters will be Special Summoned face-down to Player 1's field.

Player 1's "All-Out Attacks" will then again flip the two monsters face-up, causing both their effects to activate.

The effect of "Hiro's Shadow Scout" will again make the opponent draw 3 cards.

"Morphing Jar #2" will continue to return the two monsters to the Deck and reset them face-down onto the field, where "All-Out Attacks" will flip them.

This infinite loop repeats until Player 2 has drawn close to their whole Deck, at which point the effect of "Hiro's Shadow Scout" will force Player 2 to draw when they do not have enough cards in their Deck. This will cause Player 2 to lose the Duel due to a Deck out.

The effect of "Morphing Jar #2" will return both flipped monsters back to the Deck, and Player 1 will then reveal cards from the top of his/her Deck until revealing two monsters. Since the only two monsters in Player 1's Deck are the two that were just returned, they will be the ones revealed.

The two revealed monsters will be Special Summoned face-down to Player 1's field.

Player 1's "All-Out Attacks" will then again flip the two monsters face-up, causing both their effects to activate.

The effect of "Needle Worm" will again make the opponent mill 5 cards.

"Morphing Jar #2" will continue to return the two monsters to the Deck and reset them face-down onto the field, where "All-Out Attacks" will flip them.

This infinite loop repeats until Player 2 has milled their whole Deck, at which point the effect of "Needle Worm" ceases to cause the opponent to mill any cards. The loop now has no net change.

At this point, just as with infinite loops with no net change, the card that began the loop, "All-Out Attacks", would be destroyed by game mechanics. Once Player 1 ends their turn, Player 2 will be unable to draw a card during their Draw Phase and will lose the Duel.

Light and Darkness Dragon

If this ruling were not in place, infinite loops would occur with many mandatory Trigger Effects. For example, the following would happen during the opponent's End Phase if that player controls "Judgment Dragon":

The mandatory effect of "Judgment Dragon" activates to send cards from the Deck to the Graveyard.

The mandatory effect of "Light and Darkness Dragon" is Chained, negating the effect of "Judgment Dragon" and increasing its own ATK and DEF by 500.

The mandatory effect of "Judgment Dragon" activates to send cards from the Deck to the Graveyard.

The mandatory effect of "Light and Darkness Dragon" is Chained, negating the effect of "Judgment Dragon" and increasing its own ATK and DEF by 500.

The above sequence would repeat infinitely.

In the anime

The anime shows two infinite loops with net change, both caused by Yami Yugi.

In episode 67 of Yu-Gi-Oh!, Yami Yugi used the effects of Strings' "Slifer the Sky Dragon", "Revival Jam", and "Card of Safe Return" against him by attacking "Revival Jam", causing it to regenerate, then taking control of it by "Brain Control" so that while it regenerates, it does so on Yami's side of the field, forcing "Slifer" to attack and destroy "Revival Jam" over and over. This caused "Card of Safe Return" to make Strings continuously draw from his Deck until he got a Deck out and lost the Duel.